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Estimating unit cell volumes from powder diffraction data: the triclinic case
Author(s) -
Smith G. S.
Publication year - 1976
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889876011850
Subject(s) - triclinic crystal system , unit (ring theory) , crystallography , powder diffraction , diffraction , materials science , chemistry , crystal structure , mathematics , optics , physics , mathematics education
In the computer indexing of powder diffraction patterns, an advance estimate of the volume of the unit cell is extremely valuable. This paper describes a method for estimating it directly from powder‐pattern data for the case of triclinic materials. The method involves an easily prepared graphical plot, the slope of which is proportional to the unit‐cell volume. First, the diffraction lines are numbered consecutively, starting with the largest d value ( N = 1). A plot is then made of 1/ N versus d 3 . Theoretically, the resulting line has a slope of 3/(2π V ) = 0.4775/ V for triclinic compounds, where V is the unit‐cell volume. Examination of the graphs plotted for a number of triclinic materials where the experimental data are of high quality shows that the slope consistently falls around 0.60/ V . Hence, the volume of the unit cell and/or the calculated density can be estimated. In addition, this analysis gives a numerical measure of the fraction of possible diffraction lines actually observed.